Question

Using a straightedge and compass, construct the perpendicular bisector of FG

Answer 1

The other guy explains it, but this should basically be what it looks like

Explanation:

make A and B F and G, ignore P and Q

Answer 2

This is how I learned.
Place a point above the line segment. Open the compass so that you can create arcs on the line segment. One arc should intersect on the right side, the other on the left. Name these points (A and B, for example). Move the compass to one point. Use the same radius in the compass and make an arc below the line segment. Then move the compass to the opposite point and make another arc (with the same radius). The two arcs should intersect. Draw a line from the point above the line segment to the new intersection and you have your perpendicular bisector.